https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Periods Of Ducci sequences and odd solutions to a Pellian equation https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:46758 D:(a1,a2,…,an)↦(|a1−a2|,|a2−a3|,…,|an−a1|). Such a sequence is eventually periodic and we denote by P(n) the maximal period of such sequences for given n . We prove a new upper bound in the case where n is a power of a prime p≡5(mod8) for which 2 is a primitive root and the Pellian equation x2−py2=−4 has no solutions in odd integers x and y.]]> Wed 30 Nov 2022 08:41:27 AEDT ]]> Lower bounds for periods of Ducci sequences https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:40854 Tue 19 Jul 2022 13:07:16 AEST ]]> Explicit Drinfeld moduli schemes and Abhyankar’s generalized iteration conjecture https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:40248 k be a field containing Fq. Let ψ be a rank r Drinfeld Fq[t]-module determined by ψt(X) = tX + aXq+···+ar−1Xqr−1+Xqr, where t, a₁,...,ar−1 are algebraically independent over k. Let n ∈ Fq[t] be a monic polynomial. We show that the Galois group of ψₙ(X) over k(t, a₁,...,ar−1) is isomorphic to GLr(Fq[t]/nFq[t]), settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level tn. Video. For a video summary of this paper, please visit https://youtu.be/TInrNq02-UA.]]> Thu 28 Jul 2022 11:09:26 AEST ]]> Heights and isogenies of Drinfeld modules https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:39218 Fri 27 May 2022 11:30:35 AEST ]]> Drinfeld modular polynomials in higher rank II: Kronecker congruences https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:40246 Fri 08 Jul 2022 13:23:56 AEST ]]> Multiplicative orders of Gauss periods and the arithmetic of real quadratic fields https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:39325 −1 in a finite field by exploiting a link to the arithmetic of real quadratic fields.]]> Fri 03 Jun 2022 15:42:38 AEST ]]>